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Simplifying 0 = -4.9t2 + 50t + 11 Reorder the terms: 0 = 11 + 50t + -4.9t2 Solving 0 = 11 + 50t + -4.9t2 Solving for variable 't'. Combine like terms: 0 + -11 = -11 -11 + -50t + 4.9t2 = 11 + 50t + -4.9t2 + -11 + -50t + 4.9t2 Reorder the terms: -11 + -50t + 4.9t2 = 11 + -11 + 50t + -50t + -4.9t2 + 4.9t2 Combine like terms: 11 + -11 = 0 -11 + -50t + 4.9t2 = 0 + 50t + -50t + -4.9t2 + 4.9t2 -11 + -50t + 4.9t2 = 50t + -50t + -4.9t2 + 4.9t2 Combine like terms: 50t + -50t = 0 -11 + -50t + 4.9t2 = 0 + -4.9t2 + 4.9t2 -11 + -50t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -11 + -50t + 4.9t2 = 0.0 Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -2.244897959 + -10.20408163t + t2 = 0 Move the constant term to the right: Add '2.244897959' to each side of the equation. -2.244897959 + -10.20408163t + 2.244897959 + t2 = 0 + 2.244897959 Reorder the terms: -2.244897959 + 2.244897959 + -10.20408163t + t2 = 0 + 2.244897959 Combine like terms: -2.244897959 + 2.244897959 = 0.000000000 0.000000000 + -10.20408163t + t2 = 0 + 2.244897959 -10.20408163t + t2 = 0 + 2.244897959 Combine like terms: 0 + 2.244897959 = 2.244897959 -10.20408163t + t2 = 2.244897959 The t term is -10.20408163t. Take half its coefficient (-5.102040815). Square it (26.03082048) and add it to both sides. Add '26.03082048' to each side of the equation. -10.20408163t + 26.03082048 + t2 = 2.244897959 + 26.03082048 Reorder the terms: 26.03082048 + -10.20408163t + t2 = 2.244897959 + 26.03082048 Combine like terms: 2.244897959 + 26.03082048 = 28.275718439 26.03082048 + -10.20408163t + t2 = 28.275718439 Factor a perfect square on the left side: (t + -5.102040815)(t + -5.102040815) = 28.275718439 Calculate the square root of the right side: 5.317491743 Break this problem into two subproblems by setting (t + -5.102040815) equal to 5.317491743 and -5.317491743.Subproblem 1
t + -5.102040815 = 5.317491743 Simplifying t + -5.102040815 = 5.317491743 Reorder the terms: -5.102040815 + t = 5.317491743 Solving -5.102040815 + t = 5.317491743 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.102040815' to each side of the equation. -5.102040815 + 5.102040815 + t = 5.317491743 + 5.102040815 Combine like terms: -5.102040815 + 5.102040815 = 0.000000000 0.000000000 + t = 5.317491743 + 5.102040815 t = 5.317491743 + 5.102040815 Combine like terms: 5.317491743 + 5.102040815 = 10.419532558 t = 10.419532558 Simplifying t = 10.419532558Subproblem 2
t + -5.102040815 = -5.317491743 Simplifying t + -5.102040815 = -5.317491743 Reorder the terms: -5.102040815 + t = -5.317491743 Solving -5.102040815 + t = -5.317491743 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.102040815' to each side of the equation. -5.102040815 + 5.102040815 + t = -5.317491743 + 5.102040815 Combine like terms: -5.102040815 + 5.102040815 = 0.000000000 0.000000000 + t = -5.317491743 + 5.102040815 t = -5.317491743 + 5.102040815 Combine like terms: -5.317491743 + 5.102040815 = -0.215450928 t = -0.215450928 Simplifying t = -0.215450928Solution
The solution to the problem is based on the solutions from the subproblems. t = {10.419532558, -0.215450928}
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